Here we begin a detailed treatment of predicate logic and quantifiers. The language of predicate logic is introduced, as well as its use in translating English into formal notation and the way negation works in predicate logic. We now put together the previous discussions of argument diagramming, supplying suppressed material, rebutting premises, and rebutting inferences to show how to write a convincing rebuttal of a natural language argument making use of the formal techniques developed so far. The supplementary sections continue the application of logic to computer science and linguistics, and introduce new paradoxes as well as a discussion of philosophical questions concerned with the infinite.

Formal topics:

• Formalization in Predicate
• Consistent and contradictory statements, etc.

Informal topics:

• Rebuttal: Putting it all together
• A little more on negation

Supplementary topics:

• Hempel's paradox
• The LSAT
• BASIC
• Linguistics: rewrite rules
• Aristotle on Infinity
• Puzzles